Proactive Secret Sharing (PSS) allows secret data to be securely distributed among a group of computing devices (also referred to as players or parties in multiparty computation (MPC) literature) in such a way that if an adversary compromises no more than a fixed fraction of the computing devices, the adversary will not gain any information about the data and cannot cause data corruption.
There are several published PSS schemes (see the List of Incorporated Cited Literature Reference Nos. 1, 2, 6, 8, 10, and 11 for a description of the PSS schemes). Out of the published PSS protocols that are secure against active adversaries, the best communication complexity is O(n3) per secret (where n is the number of computing devices).
Thus, a continuing need exists for a PSS protocol that improves computational complexity.